Gravity doesnt warp space-time fabric. Energy(which includes mass) does. The spacetime near any massive object is bent, in the sense that it differs from the usual kind of geometry. This warping of geometry is what appears to us as gravity. In warped spacetime, the usual straight lines or "Geodesics" are not what they used to be. Objects moving in a straight line(in the 4-d spacetime) appear to be moving in a curved line to us in the 3 space dimentions.

So, I guess my question is
How does the geometry warping appear as gravity?
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Gravity = accelerated massSo, how does the bending of space-time by mass appear as an intrinsic acceleration?
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For example:
Mass “m1” exists in space-time near another mass “m2”
Both masses are stationary relative to each other.
Mass “m1” bends space-time near mass “m2” and vice versa.

How does this explain the gravitational effects between the 2 masses “m1” and m2”?

As I have already said, a straight line in spacetime would not appear as a straight line in space to us. Objects always travel in straight lines in spacetime, but, this straight line in spacetime is not a straight line in space. Any deviation from a straight line in space indicates acceleration.

Particles follow "geodesics" in spacetime. On a curved 2D surface, a geodesic would be the shortest path between two points on the surface--for example, on a sphere the shortest path between points would be a section of the great circle that passes through both points. In curved spacetime, a geodesic is the worldline between two events with the greatest proper time (time as measured by a clock that follows that worldline). For example, in the "twin paradox" the twin who doesn't accelerate is the one who follows a geodesic, that's why he'll be older than his brother who did accelerate when they reunite. Planets in orbit are also following geodesics through the curved spacetime around the sun, although I don't know the details of how you'd show this.

Remember that one second of time is equivalent to 300,000 kms of space. In a space-time diagram drawn to scale the orbit of the Earth, spiralling through space-time, would be 1 A.U. across but I light year in 'pitch'. Therefore the amount of curvature is actually very slight.

Just some added notes. You can draw a space-time diagram by plotting position as a funciton of time. You usually do this on a flat sheet of paper.

What if you did this plot on a curved sheet of paper? Specifically, one curved like the surface of a sphere.

It's too hard to draw pictures on the internet, but if you manage to carry out this expeirment, you'll see that the worldlines of neighboring particles act a lot like they attracted each other - even though one is just drawing "straight" lines on a curved surface.

"Straight" lines in this context are the shortest paths that join two points while remianing entirely on the curved surface (it's not allowable to leave the surface). They are also called geodesics.

A picture or two might really help, but you'll need to go to a textbook to find one AFAIK - I haven't run across any on the internet, and ascii is certainly not up to the job.